Studying the streamlining of a blunted body by a vibrational-nonequilibrium dissociated gas

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 30, No. 6, pp. 139–145, November–December, 1989.     

1,1-Dichloro-2,2,2-trihaloethyl Isocyanates and N-(1-Chloro-2,2,2-trihaloethylidene)urethanes in the Synthesis of 4-Trihalomethyl-2H-1,3-benzoxazin-2-ones

4-Trihalomethyl-2H-1,3-benzoxazin-2-ones have been synthesized by the reaction of 1,1-dichloro-2,2,2-trihaloethyl isocyanates or N-(1-chloro-2,2,2-trihaloethylidene)urethanes with 3-dialkylamino(alkoxy)phenols. The character of the products from the addition of nucleophiles has been shown to depend on the nature of the nucleophile and the trihalomethyl group.     

Unusual Cyclization of N-(1-Aryl-1-chloro-2,2,2-trifluoroethyl)-N'-(p-tolyl)-carbodiimides in the Presence of Triethylamine

1-Aryl-1-chloro-2,2,2-trifluoroethyl)-N'-(p-tolyl)carbodiimides treated with triethylamine undergo intramolecular cyclization into 4-aryl-6-methyl-2-triethylammonio-4-trifluoromethyl-4-dihydroquinazolidines.     

A Facile Synthesis of Functionalized 1,2,6,7-Tetrahydroimidazo[1,5-c]pyrimidine-3,5-diones

A Pd-mediated hydrogenation of ethyl 6-azidomethyl-1,2,3,4-tetrahydro-4-R-2-oxo-5-pyrimidinecarboxylates leads to the corresponding ethyl 6-aminomethyl1,2,3,4-tetrahydro-4-R-2-oxo-5-pyrimidinecarboxylates. The latter react with bis(trichloromethyl)carbonate, yielding the title ethyl 1,2,3,5,6,7-hexahydro-7-R-3,5-dioxoimidazo[1,5-c]pyrimidine-8-carboxylates.

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Heterocyclizations of Functionalized Heterocumulenes with C,N- and C,O-Dinucleophiles: II.* Reaction of 1-Chloro- and 1,1-Dichloroalkyl Isocyanates and 1-Chloroalkylidenecarbamates with 2-Bensothiazolylacetonitrile, 2-Benzothiazolylacetates,and Bis(2-benzothiazolyl)methane

1-Chloroalkyl isocyanates react with 2-R-methylbenzothiazoles [R = CN, C(O)OAlk, 2-benzothiazolyl] in the presence of triethylamine to give 4-R-2,3-dihydro-1H-pyrimido[6,1-b][1,3]benzothiazol-1-ones. The same reaction at elevated temperature in the absence of a base yields isomeric 4-R-2,3-dihydro-1H-pyrimido[6,1-b][1,3]benzothiazol-3-ones. 4-R-1H-Pyrimido[6,1-b][1,3]benzothiazol-1-ones are formed in the reaction of 1,1-dichloroalkyl isocyanates or methyl 1-chloroalkylidenecarbamates with 2-benzothiazolylacetonitrile or bis(2-benzothiazolyl)methane.     

Transport coefficients of a dissociating gas

The calculation of the transport coefficients of a dissociating gas involves fundamental difficulties which arise when the internal degrees of freedom of the molecules are taken strictly into account. In practical calculations extensive use is made of the approximation proposed in [1], in the context of which the dependence of the diffusion velocity of the molecule on its internal state is totally neglected. In this case the expressions for the stress tensor and the diffusion velocities coincide with the corresponding expressions for a mixture of structureless particles; in the expression for the heat flux the diffusion transport of internal energy is taken only approximately into account. Here, analytic expressions for the diffusion velocities, heat flux and stress tensor are obtained without introducing simplifying assumptions. The calculation method is based on the results of [2], in which an approximate method of calculating the transport coefficients of a multicomponent mixture of structureless particles was proposed, and [3], in which the transport coefficients of a rotationally excited gas were calculated. The relations obtained are analyzed and compared with the existing results; their accuracy is estimated. A closed system of equations of gas dynamics is presented for a number of cases of practical importance.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–165, January–February, 1987.     

Quadrature formulas with minimum error for certain classes of functions

Problems connected with optimum quadrature formulas for the function classes H and H ⁿ are investigated.Translated from Matematicheskie Zametki, Vol. 3, No. 5, pp. 577–586, May, 1968.